Among the options, according to the Journal, will be provisions to stabilize Obamacare's individual insurance exchanges and a longer phase out of the ACA's federal funding to expand Medicaid.

The stabilization of the insurance exchanges could also be a separate bill, according to the report. Such a move would allow the Senate more time to craft their own healthcare overhaul.

Additionally, the report said Senate GOP leaders hope to write a bill and get it to the Congressional Budget Office to be scored by the end of the week. Leaders also want a vote on a bill before the week-long July 4 recess.

Senate GOP members have said they are planning to write their own version of a bill, diverging from the House's American Health Care Act. The expedited process is key to getting a healthcare bill done before the month-long August recess. A crowded legislative calendar in September could derail any reform for months.

Passing a healthcare bill in the Senate is also a politically fraught effort given that Senate Majority Leader Mitch McConnell can only afford to lose two votes on the bill given the reconciliation process the Republicans are using.

Currently, more moderate members of the Senate GOP are pushing for more funding for Medicaid and added funding for tax credits to help people purchase coverage. On the other hand, conservative members of the group, such as Sen. Ted Cruz and Rand Paul, are pushing for deeper funding cuts and a more complete repeal of Obamacare.